67-year-old Tony Overheu, a former sheep farmer, said he squashed lemon meringue pie in Joyce's face during a press conference because of his views supporting same-sex marriage.
Overheu released a statement which accused Qantas and other companies that support marriage equality of "corporate bullying aimed at social engineering".
He said he chose lemon meringue from a cake shop the night before because it "appeared to be the softest, least likely to do any injury".
Police have charged him with giving officers false details and are still investigating.
Overheu said: "Our family is outraged, my wife is down my throat, I didn't understand that I'd breached the state's criminal code and the police are dealing with it. Clearly I regret that."
Joyce, 50, confirmed the apology, but said: "I'm not sure there's any regret at the issue that has occurred.
"My intention is to send a message that this type of behaviour isn't acceptable and I have every intention of pressing charges.
"Nobody should be... intimidated, nobody should be bullied, nobody should certainly have an incident like occurred yesterday to try to stop people having that freedom of speech."
Joyce has been criticised by government ministers for joining 30 chief executives of high-profile Australian companies who wrote a letter to Prime Minister Malcolm Turnbull in March calling for Parliament to legalise same-sex marriage.
Immigration minister Peter Dutton, a gay marriage opponent, told the CEOs to "stick to their knitting" and keep out of the political debate.